一、課程說明(Course Description) 
<br>This is a mandatory mathematics course for students in the second year of study in the  ESS 
<br>department. The topics of this course include: 
<br>1) Ordinary Differential Equations: 1st order ODEs, 2nd order ODEs, higher order ODEs, systems 
<br>of ODEs 
<br>2) Special functions and power series method 
<br>3) Laplace Transform 
<br>* 課程預備知識: 需已修習過微積分 
<br>
<br>二、指定用書(Text Books) 
<br>Zill & Wright, "Advanced Engineering Mathematics", 5th Ed., Jones & Bartlett (2014) 
<br>
<br>三、參考書籍(References) 
<br>Michael D. Greenberg, "Advanced Engineering Mathematics" 2nd ed., 
<br>(1998 by Prentice-Hall International, 2006 by Pearson Education) 
<br>
<br>
<br>四、教學方式(Teaching Method) 
<br>3 hours lecture per week。 
<br>上課時間: 每週二及週五上午 8:30-9:50 (課程中間不下課休息) 
<br>
<br>Office Hours,
<br>Tuesday, 1:00 - 2:00 pm 
<br>
<br>五、教學進度(Syllabus) 
<br>Week 1: Introduction to Differential Equation, definition of basic terminology 
<br>
<br>Week 2,3: Linear ODE (homogeneous, non-homogeneous): Euler's integrating factor method, 
<br>Lagrange's variations of parameter method, Bernoulli equation, Riccati equation, d'Alembert-
<br>Lagrange equation, Separable equation, exact equation and integrating factors. 
<br>
<br>Week 4,5,6: Linear ODE of 2nd order or higher, linear independent/dependent, Wronskian, basis 
<br>set of solution of DE, existence and uniqueness for Initial-Value Problem, homogeneous 
<br>equation with constant coefficients (characteristic equation, distinct roots, repeated roots ), 
<br>harmonic oscillator (free oscillation) 
<br>
<br>Week 7,8,9: Linear nonhomogeneous equation with constant coefficients (method of 
<br>undetermined coefficients, method of inverse operators), Forced harmonic oscillator, system of 
<br>linear ODE with constant coefficients, Linear ODE with variable coefficients (Cauch-Euler 
<br>equation, Method of reduction of order, Method of variation of parameters) 
<br>
<br>Week 10,11: power series method, Method of Frobenius 
<br>
<br>Week 12,13: Legendre equation, Gamma function, Bessel equation, modified Bessel equation, 
<br>exponential integral, equations reducible to Bessel equations 
<br>
<br>Week 14,15: Laplace transform, inverse Laplace transform, special functions, application to the 
<br>solution of ODE. 
<br>
<br>
<br>六、成績考核(Evaluation) 
<br>Homeworks (25%)
<br>First Midterm Exam (25%) 
<br>Second Midterm Exam (25%)
<br>Final Exam (25%)
<br>